For example, Kozlov [1]} proved that \(I(C_n)\)  is homotopy equivalent to a wedge sum of spheres. So, it follows from Theorem REF  that \(I({L_m}[{C_n}])\)  with \(m \ge 4\)  is homotopy equivalent to a wedge sum of spheres.
Remark that \({L_m}[{C_n}]\)  contains a cylindrical square grid graph as a subgraph which is obtained from \({L_m}[{C_n}]\)  by removing edges.
Furthermore, we determined the homotopy type of \(I({L_m}[{H}])\)  for any \(m \ge 1\)  and a graph \(H\)  such that \(I(H)\)  is homotopy equivalent to \(n\)  copies of \(k\) -dimensional spheres.
We denote the \(d\) -dimensional sphere by \(S^{d}\)  and a wedge sum of \(n\)  copies of CW complex \(X\)  by \(\bigvee _{n} X\) .
